Divide 18 to both sides and you get -12
Answer:
Her average rate of speed is 53 mph.
Step-by-step explanation:
(x^2– 8)^2 + x^2 – 8 = 20
x=
The possible values of x that satisfy the equation are
x = ±√3 and x = ±2√3.
Here, we have,
To find a value of x that is a solution to the equation, we need to solve the equation for x.
Let's go through the steps:
Start with the given equation:
(x² - 8)² + x² - 8 = 20
Expand the squared term (x² - 8)²:
(x² - 8)(x² - 8) + x² - 8 = 20
Simplify:
(x⁴ - 16x² + 64) + x² - 8 = 20
Combine like terms:
x⁴ - 16x² + x² + 64 - 8 = 20
Simplify:
x⁴ - 15x² + 56 = 20
Rearrange the equation to bring all terms to one side:
x⁴ - 15x²+ 56 - 20 = 0
Simplify:
x⁴ - 15x² + 36 = 0
Now, we have a quadratic equation in terms of x².
Let's substitute y = x² to simplify further:
y² - 15y + 36 = 0
Solve the quadratic equation for y:
(y - 3)(y - 12) = 0
This gives us two possible values for y:
y - 3 = 0 --> y = 3
y - 12 = 0 --> y = 12
Substitute back y = x²:
For y = 3:
x² = 3 --> x = ±√3
For y = 12:
x² = 12 --> x = ±√12 = ±2√3
So, the possible values of x that satisfy the equation are x = ±√3 and x = ±2√3.
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Answer:
x = 2 sqrt(3) or x = -2 sqrt(3) or x = sqrt(3) or x = -sqrt(3)
Step-by-step explanation:
Solve for x:
-8 + x^2 + (x^2 - 8)^2 = 20
Expand out terms of the left hand side:
x^4 - 15 x^2 + 56 = 20
Subtract 20 from both sides:
x^4 - 15 x^2 + 36 = 0
Substitute y = x^2:
y^2 - 15 y + 36 = 0
The left hand side factors into a product with two terms:
(y - 12) (y - 3) = 0
Split into two equations:
y - 12 = 0 or y - 3 = 0
Add 12 to both sides:
y = 12 or y - 3 = 0
Substitute back for y = x^2:
x^2 = 12 or y - 3 = 0
Take the square root of both sides:
x = 2 sqrt(3) or x = -2 sqrt(3) or y - 3 = 0
Add 3 to both sides:
x = 2 sqrt(3) or x = -2 sqrt(3) or y = 3
Substitute back for y = x^2:
x = 2 sqrt(3) or x = -2 sqrt(3) or x^2 = 3
Take the square root of both sides:
Answer: x = 2 sqrt(3) or x = -2 sqrt(3) or x = sqrt(3) or x = -sqrt(3)
1. Two consecutive integers means that the values are whole numbers and they are located right after the other (eg. 2, 3).
Now, let us call the smaller value x. The consecutive value will be one greater than x, thus the larger value may be written as x + 1.
2. We know that the product of the two values is 420. Given that the smaller value is x and the larger value is x + 1, we can write this as:
x(x + 1) = 420
3. Now we can expand to get:
x^(2) + x = 420
4. Now subtract 420 from both sides to get:
x^(2) + x - 420 = 0
Therefor, the constant of the quadratic expression is -420.
Answer:
∠ ABC = 90°
Step-by-step explanation:
∠ ABC is the angle in a semi circle and is right, that is
∠ ABC = 90°